Chapter 2.1, Problem 90AYU

To determine

To express:Thearea of the given isosceles right triangle as a function oflength of one of its equal side.

Answer to Problem 90AYU

Area can be expressed as $A\left(x\right)=\frac{1}{2}{x}^2$ .

Explanation of Solution

Given information:

Length of one of the equal side is $x$ .

Calculation:

Isosceles right triangle must have two equal sides.

The equal sides should be the base and height of the triangle.

As hypotenuse is the largest side of right triangle.

Now, consider a triangle as shown:

  

Now, area of a right triangle is half of the product of its base and height.

Let us consider the area function be $A\left(x\right)$ .

Therefore, the area can be expressed as shown:

  $\begin{array}{c}A\left(x\right)=\text{Base}\times \text{Height}\\ =\frac{1}{2}\times x\times x\\ =\frac{1}{2}{x}^2\end{array}$

Area can be expressed as $A\left(x\right)=\frac{1}{2}{x}^2$ .